System and method for providing an estimate of property value growth based on a repeat sales house price index

ABSTRACT

Systems, methods, and computer-readable storage media are described for estimating real estate property values based on an adjusted repeat sales model using a regularized estimator. In one exemplary embodiment, a computer-implemented method calculates data for estimating the adjustments from an aggregated level to a first disaggregated level by marking a first transaction to a second transaction using a repeat sales house price index function at the aggregated level. The method also determines, using the calculated data, a regularized estimate of the deviation between the repeat sales house price index at the aggregated level and a repeat sales house price index at the first disaggregated level. The method further calculates the repeat sales house price index at the first disaggregated level based on the determined regularized estimate of the deviation from the aggregated level.

RELATED APPLICATIONS

This is a continuation of application Ser. No. 12/954,143, filed Nov.24, 2010, which is a continuation-in-part of U.S. Pat. No. 8,407,120,issued Mar. 26, 2013, the contents of which are hereby incorporatedherein by reference in their entirety.

TECHNICAL FIELD

The present disclosure generally relates to estimating property values,and more particularly, to providing property value estimates based on arepeat sales model using a regularized estimator.

BACKGROUND

Financial institutions and businesses involved with sales of propertyhave long tried to estimate values of property accurately. Accurateestimation serves many important purposes. For example, financialinstitutions use property value estimates as one of the key factors incalculating the loan to value (LTV) ratio of a home. The LTV ratio isthe ratio of a first mortgage (or the total of all mortgage liens(TLTV)) to the appraised or estimated value of the real property. TheLTV ratio is an important calculation used by financial institutions toassess lending risks. For example, as the LTV ratio of a propertyincreases, the likelihood of loan default increases. In addition, when adefault does occur, the higher the LTV ratio, the greater the potentialfinancial loss to the financial institution. Moreover, financialinstitutions may “mark-to-market” their portfolio of outstanding loansto determine the current LTV ratios of the mortgages. Mark-to-market isan accounting methodology used to calculate current LTV ratio ofoutstanding loans. Accordingly, the accuracy of the estimated value ofreal estate used to calculate the LTV ratio is critical.

One technique for estimating the value of real estate utilizes a repeatsales index. A repeat sales index may be used to identify housing marketconditions and the amount of equity homeowners have gained through houseprice appreciation. The index itself is a composite of changes inindividual home prices within a geographical region, such as amunicipality, zip code, county, region, or state. The data used in therepeat sales index may comprise successive selling prices and the saledates for the same property (e.g., a residential home). By using pricingof the same property, the repeat sales index eliminates the inherentbias in price changes that are not due to the true house price change,but due to external factors such as, for example, consumer trends forbigger houses.

The basic repeat sales index may be improved through the use of datafrom refinance transactions, in addition to data from purchasetransactions, in forming repeat sales indices, thereby increasing thesize of the estimation sample and the timeliness of the evaluationsample. Moreover, as disclosed in U.S. Pat. No. 6,401,070, the data usedin a repeat sales index may be weighted to provide particular importanceto one set of data over another. The content of U.S. Pat. No. 6,401,070is incorporated herein by reference in its entirety.

There are qualitative differences between house price data derived frompurchase transactions and from refinance transactions. Purchasetransactions typically involve arms-length agreements in which theincentives of the parties will tend to result in an unbiased salesprice, and the information of the three parties (buyer, seller, andappraiser) will tend to result in greater accuracy in ascertaining thevalue of the property, Refinance transactions, on the other hand, havevaluation based solely on an appraisal and consequently are subject toseveral sources of bias. For example, incentive biases in appraisalsarise because appraisers are motivated to arrive at valuations that canmake the refinance transaction successful. Selection biases arisebecause, particularly in a down market, the properties that are eligiblefor refinance are more likely to be those that have appreciated relativeto the market as a whole.

A repeated sales index that factors in such biases to the data isgenerically referred to as a weighted repeat sales index (WRSI). WRSIalso refers to indexes that include refinance transactions as well asproperty sale transactions, and indexes with and without weights on thetransactions. As disclosed in U.S. Pat. No. 6,401,070, the WRSI may beexpressed as:log(P _(s) /P _(t))=I _(s) −I _(t) +d _(s2) R _(s2) −d _(t1) Rt1÷ξ  (1)

Here, the variable P_(t) is the first transaction price, P_(s) is thesecond transaction price, I_(t) is the log house price index (HPI) valueat time t, R_(t1) is equal to one (1) if the first transaction is arefinance and equal to zero (0) otherwise, R_(s2) is equal to one (1) ifthe second transaction is a refinance and equal to zero (0) otherwise,d_(t1) is a coefficient representing the first transaction refinance(REFI) bias at time t, d_(s2) is coefficient representing the secondtransaction refinance (REFI) bias at time s, and ξ is the error term. Inessence, the refinance bias terms measure the difference in appreciationbetween purchase and refinance transactions at the two dates.Accordingly, the WRSI model of equation (1) allows for time varyingdifferences between refinance and purchase transactions, therebyimproving index accuracy.

As used herein, “aggregated level” refers to a geographic regioncomprised of more than one smaller geographic regions. For example, astate may be an aggregated level of counties and zip codes. As usedherein, “disaggregated level” refers to a geographic region that may beincluded in an aggregated level. For example, a county and a zip codemay be disaggregated levels of a state.

The HPI and REFI values that that are used in the WRSI model may beestimated using an ordinary least square (OLS) regression. However, HPIand REFI index estimation using OLS yields excessively volatile andinaccurate estimates, especially at disaggregated levels.

Accordingly, systems and methods are needed that provide a betterestimation of the HPI and REFI values that are used in a home priceindex model. Systems and methods consistent with the present inventionaddress the difficulties discussed above by providing a regularized,adjusted WRSI that calculates a more accurate estimated value of realestate growth rates at aggregated and disaggregated levels, among otherthings.

SUMMARY

Consistent with the present invention, as embodied and broadly describedherein, systems and methods are disclosed for providing an regularized,adjusted weighted repeat sales index.

In one exemplary embodiment, a method for estimating a weighted repeatsales index using a regularized estimator is disclosed. The methodincludes calculating data for estimating the adjustments from anaggregated level to a first disaggregated level by marking a firsttransaction to a second transaction using a repeat sales house priceindex function at the aggregated level. The method also includesdetermining, using the calculated data, a regularized estimate of thedeviation between the repeat sales house price index at the aggregatedlevel and a repeat sales house price index at the first disaggregatedlevel. The method further includes calculating the repeat sales houseprice index at the first disaggregated level based on the determinedregularized estimate of the deviation from the aggregated level.

In another embodiment, a system for estimating a weighted repeat salesindex using a regularized estimator is disclosed. The system includesmeans for calculating data for estimating the adjustments from anaggregated level to a first disaggregated level by marking a firsttransaction to a second transaction using a repeat sales house priceindex function at the aggregated level. The system also includes meansfor determining, using the calculated data, a regularized estimate ofthe deviation between the repeat sales house price index at theaggregated level and a repeat sales house price index at the firstdisaggregated level. The system further includes means for calculatingthe repeat sales house price index at the first disaggregated levelbased on the determined regularized estimate of the deviation from theaggregated level. Similarly, a regularized estimated at a 2^(nd) levelof disaggregation and additional levels of disaggregation beyond the2^(nd) can be calculated.

In yet another embodiment, a computer-readable medium including programinstructions for performing, when executed by a processor, a method forestimating a weighted repeat sales index using a regularized estimatoris disclosed. The method includes calculating data for estimating theadjustments from an aggregated level to a first disaggregated level bymarking a first transaction to a second transaction using a repeat saleshouse price index function at the aggregated level. The method alsoincludes determining, using the calculated data, a regularized estimateof the deviation between the repeat sales house price index at theaggregated level and a repeat sales house price index at the firstdisaggregated level. The method further includes calculating the repeatsales house price index at the first disaggregated level based on thedetermined regularized estimate of the deviation from the aggregatedlevel.

It is to be understood that both the foregoing general description andthe following detailed description are exemplary and explanatory onlyand are not restrictive of the invention, as described. Further featuresand/or variations may be provided in addition to those set forth herein.For example, embodiments of the present invention may be directed tovarious combinations and subcombinations of several further featuresdisclosed below in the detailed description.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings, which are incorporated in and constitute apart of this specification, illustrate various features, embodiments andaspects consistent with the invention and, together with thedescription, explain advantages and principles of the invention. In thedrawings,

FIG. 1 is a block diagram of an exemplary overview of a property valueestimation system, consistent with the principles of the presentinvention;

FIG. 2 is an exemplary flowchart for a regularized, adjusted WRSImethodology, consistent with the principles of the present invention;and

FIG. 3 illustrates examples of plots of conventional, spline, andregularized, adjusted WRSI quarterly house price growth.

DESCRIPTION OF THE EMBODIMENTS

Reference will now be made in detail to various embodiments of theinvention, examples of which are illustrated in the accompanyingdrawings. Wherever convenient, similar reference numbers will be usedthroughout the drawings to refer to the same or like parts. Theimplementations set forth in the following description do not representall implementations consistent with the claimed invention. Instead, theyare merely some examples of systems and methods consistent with theinvention.

Systems and methods consistent with principles of the present inventionaddress the limitations and disadvantages of traditional WRSI forestimating house price values. Systems and methods consistent withprinciples of the present invention estimate real estate property valuesbased on an adjusted repeat sales model.

FIG. 1 is a block diagram illustrating an exemplary system architecturefor a computer system with which embodiments consistent with the presentinvention may be implemented. In the embodiment shown, computer system100 includes a bus 102 or other communication mechanism forcommunicating information, and a processor 104 coupled to bus 102 forprocessing information. Computer system 100 may also include a mainmemory, such as a random access memory (RAM) 106 or other dynamicstorage device, coupled to bus 102 for storing information andinstructions to be executed by processor 104. RAM 106 also may be usedto store temporary variables or other intermediate information producedduring execution of instructions by processor 104. Computer system 100may further include a read only memory (ROM) 108 or other static storagedevice coupled to bus 102 for storing static information andinstructions for processor 104. A storage device 110, such as a magneticdisk or optical disk, may also be provided and coupled to bus 102 forstoring information and instructions.

Computer system 100 may be coupled via bus 102 to a display 112, such asa thin film transistor liquid crystal display (TFT-LCD), for displayinginformation to a computer user. An input device 114, such as a keyboardincluding alphanumeric and other keys, is coupled to bus 102 forcommunicating information and command selections to processor 104.Another type of user input device is a cursor control 116, such as amouse, a trackball, or cursor direction keys for communicating directioninformation and command selections to processor 104 and for controllingcursor movement on display 112.

In the embodiment shown, computer system 100 may access data from realestate database 130 and execute one or more sequences of one or moreinstructions contained in main memory 106. Both the data from realestate database 130 and the instructions may be read into main memory106 from another computer-readable medium, such as storage device 110,Data from real estate database 130 may comprise refinance and purchasetransaction data 132, regularized estimation data 134, and regularizedwith refinance and purchase transaction data 136.

The instructions may implement regularized, adjusted WRSI models, asdiscussed in greater detail below. Execution of the sequences ofinstructions contained in main memory 106 causes processor 104 toperform operations consistent with the process steps described herein.In one alternative implementation, hardwired circuitry may be used inplace of or in combination with real estate database and/or softwareinstructions to implement the invention. Thus implementations of theinvention are not limited to any specific combination of hardwarecircuitry and software.

Computer system 100 may communicate with real estate database 130through a communication channel comprising, for example, alone or in anysuitable combination, a telephony-based network, a local area network(LAN), a wide area network (WAN), a dedicated intranet, wireless LAN,the Internet, and intranet, a wireless network, a bus, or otherappropriate communication mechanisms. Moreover, various combinations ofwired and/or wireless components may be incorporated into thecommunication channel. Furthermore, various combinations ofpoint-to-point or network communications may also be incorporated intothe communication channel to facilitate communication between thecomputer system 100 and the real estate database 130. All or someportions of bus 102, for example, may be implemented using suchcommunications mechanisms. Additionally, data communicated through thecommunication channel may be communicated instead through the transferof computer-readable media, such as DVDs.

The term “computer-readable medium” as used herein refers to any mediathat participates in providing instructions to processor 104 forexecution. Such a medium may take many forms, including but not limitedto, non-volatile media and volatile media. Non-volatile media includes,for example, optical or magnetic disks, such as storage device 110.Volatile media includes dynamic memory, such as main memory 106.

FIG. 2 is a flowchart for an exemplary method for estimating a weightedrepeat sales index, consistent with the present disclosure. Although themethod illustrated in FIG. 2 is illustrated as a series of steps, itwill be understood by those skilled in the art that non-dependent stepsmay be performed in a different order than illustrated, or in parallel.

In step 210, data regarding all property transactions during a period oftime may be collected and standardized. This data may include housessold and refinanced. The addresses of the sold and refinanced houses maybe standardized by matching the addresses to a U.S. postal standard sothat the same house is used. For example, if a house address for a firstsale or refinance is listed as 5400 North 22^(nd) Street and the samehouse is listed as 5400 22^(nd) Street North for a second sale orrefinance, the U.S. postal standard may standardize the addresses anddetermine that the two listed addresses are variations of the sameaddress for the same house.

In step 220, data for estimating the adjustments from aggregated todisaggregated levels are created by marking (e.g., pairing) a first realestate transaction to a second real estate transaction using a repeatsales house price index function at an aggregated level, designated byI(t). Step 220 may be skipped when estimating the aggregate level index.The pairs created from marking the first real estate transaction to thesecond real estate transaction may have equal weights, no weights, orunequal weights. If all pairs created from the first real estatetransaction and the second real estate transaction have equal weights,this may be considered equivalent to no weights because there is novariation in the weights. In addition, the estimated index may still beconsidered weighted even though there may be no associated weights orall weights may be the same.

For discussion of this embodiment, the aggregated level will be thestate level. I(t) for the state level may be defined by equation (1)discussed above. Specifically, in one embodiment, I(t) may be calculatedusing equation (1) in conjunction with regularized estimation techniquesapplied to refinance and purchase data.

Equation (1) may be rewritten to replace P_(s) with p_(i,t2), P_(t) withp_(i,t1), I_(s) with HPI_(t2(I)), I_(t) with HPI_(t1(i)), d_(s2)R_(s2)with refi2 _(i)refiprem2 _(t2(i)), d_(s1)R_(s1) with refi1 _(i)refiprem1_(t1(i)), Accordingly, equation (1) may be expressed as a model thattakes the form of:y _(i)=log(p _(i,t2) /p _(i,t1))=HPI _(t2(i)−) HPI_(t1(i))+refi2_(i)refiprem2_(t2(i))−refi1_(i)refiprem1_(t1(i))+ε_(i)  (2)where y_(i) is a transaction return, p_(i,t1) is the first transactionprice, p_(i,t2) is the second transaction price, HPI_(t1(i)) is the logindex value at time t₁, HPI_(t2(i)) is the log index value at time t₂,refiprem1 _(t1(i)) is equal to one (1) if the first transaction is arefinance and equal to zero (0) otherwise, refiprem2 _(t2(i)) is equalto one (1) if the second transaction is a refinance and equal to zero(0) otherwise, refi1 _(i) is a coefficient representing the firsttransaction refinance bias at time t₁, refi2 _(i) is coefficientrepresenting the second transaction refinance bias at time t₂, and ε_(i)is the error term.

Equation (2) may be rewritten by stacking all transaction returns as:y=Xβ+ε  (3)where y is a vector of stacked repeat transaction returnsy_(i)=log(p_(i,t2)/p_(i,t1)). X=[X1 X2 X3] is the matrix with theregressors: X1 is a N*(T−1) matrix which in each row i has a −1 incolumn t1 if the first transaction of repeat transaction i took place attime t1 and a 1 in column t2 if the second transaction of repeattransaction i took place at time t2. The last time period T does notreceive a column in matrix X1, which normalizes HPI_(T) to zero. X2 is aN*T matrix which in each row i has a −1 in column t1 if the firsttransaction of repeat transaction i has a refi flag. Similarly, X3 is aN*T matrix which in each row i has a 1 in column t2 if the secondtransaction of repeat transaction i has a refi flag. The coefficientvector β′ is [β_(HPI)′β_(refi1)′β_(refi2)′] where β_(HPI) is the HPIvector for t=1 . . . T−1, β_(refi1) is the vector of refi1 _(i)refiprem1_(t1(i)), β_(refi2) is the vector of refi2 _(i)refiprem2 _(t2(i)), and εis the vector of pricing error terms.

This regression set-up generalizes to linear splines such as describedin U.S. Pat. No. 6,401,070, by modifying the X=[X1 X2 X3] matrix alongthe appropriate lines. Specifically, for monthly knot points for HPI_(t)on the first of each month, for a date n days into month m, weight ([#days in month m]+1−n)/[# days in month m] may be put on the X columnscorresponding to the knot point on the first day of month m and weight(n−1)/[# days in month m] may be put on the knot point on the first dayof the next month after month m. This set up allows for a smoothmodeling of within month, transaction returns with index valuesestimated at monthly frequencies. This is a sensible approach given thevolatility of index values at, monthly frequencies.

At this time, parameters HPI_(t), refiprem1 _(t), and refiprem2 ₁ may beestimated using the equation:

$\begin{matrix}\; & (4) \\{\min\limits_{({{HPI}_{t},{{refiprem}\; 1_{t}},{{refiprem}\; 2_{t}}})}{\sum\limits_{i}{\left( {y_{i} - {H\; P\; I_{t\; 2{(i)}}} + {H\; P\; I_{t\; 1{(i)}}} + \mspace{256mu}{{refi}\; 2_{i}\;{refiprem}\; 2_{t\; 2{(i)}}} - {{refi}\; 1_{i}{refiprem}\; 1_{t\; 1{(i)}}}} \right)^{2}/\sigma_{ɛ}^{2}}}} & \;\end{matrix}$

Equation (4) may be represented in a compact notation such as:min_(β)σ_(ε′) ⁻²(y−Xβ)′(y−Xβ)  (5)where β may be estimated using an Ordinary Least Squares (OLS) model as:{circumflex over (β)}_(OLS)=(X′X)⁻¹ X′y.  (6)where the values of X, X′, and y are the values from equation (3).

After calculating {circumflex over (β)}_(OLS) using equation (6),{circumflex over (β)}_(OLS), in turn, may be used to estimate the valuesof HPI at time t₁ and t₂ and the values of refiprem at time t₁ and t₂.However, the {circumflex over (β)}_(OLS) value calculated using equation(6) may result in an excess HPI growth volatility that is observed usingOLS regressions.

The estimate {circumflex over (β)}_(OLS) of HPI and refi premia differsfrom the underlying true HPI and refi premia that give rise to theobserved transaction and refi prices because of the repeat transactionreturn noise ε. Specifically,{circumflex over (β)}_(OLS)−β−(X′X)⁻¹ X′ε.

The covariance matrix of this estimation error is given byvar({circumflex over (β)}_(OLS)−β)=σ_(ε) ²(X′X)⁻¹.

Two remarks are appropriate regarding this estimation error in{circumflex over (β)}_(OLS). First, the estimation error for every monthdepends on the monthly sample size of the data, and, therefore,sensitively may reflect small sample size problems for high frequencyestimation periods and detailed levels of geographical disaggregation.Second, from this expression the variance in the second difference ofHPI that is due to sample error may be determined. The second differenceof HPI is given by D²S_(HPI)β. Here S_(HPI) may be a matrix that selectsthe HPI component of β (as well as adding a zero for HPI_(T)) and D maybe the matrix that takes the first difference. Accordingly, the size ofD depends on context. The variance of the innovation to HPI growth dueto sample error is then given byvar(Δ² S _(HPI)({circumflex over (β)}_(OLS)−β))=var(D ² S_(HPI)({circumflex over (β)}_(OLS)−β))=σ_(ε) ² D ² S _(HPI)(X′X)⁻¹ S_(HPI) ′D ²′.

Some of the estimated change in HPI growth is due to sample error, notchanges in the growth of the underlying HPI. There may still beuncorrelated variance in the growth rate estimated HPI that is due tothe underlying HPI. Noting the large diagonal elements in (X′X)⁻¹ fortypical repeat home transactions data sets, the sample noise inducedchange in estimated HPI growth may be negatively autocorrelated at lagone. Moreover, for high frequency measurement intervals for HPI withsmall samples, the size of this measurement error induced excessvolatility of HPI growth is large relative to the volatility ofunderlying HPI growth.

The regularized regression approach may greatly reduce these problems byaveraging across many months given the underlying noise in individualrepeat transaction data and the volatility of changes in the growth ofHPI.

The OLS estimate {circumflex over (β)}_(OLS)=(X′X)⁻¹X′y does not takeinto account that the second difference of HPI is drawn from N(0,σ_(ΔHPI) ²), nor does it take into account that the first differences ofthe two refi premia are drawn from N(0, σ_(refi) ²).

Accordingly, the value of β may be regularized by picking {circumflexover (β)}_(reg) to minimize the expression:min_(β)σ_(ε) ⁻²(y−Xβ)′(y−Xβ)+σ_(ΔHPA) ⁻²(D ² S _(HPI)β)′(D ² S_(HPI)β)+τ_(refi) ⁻²(DS _(refi1)β)′(DS _(refi1)β)+σ_(refi) ⁻²(DS_(refi2)β)′(DS _(refi2)β).  (7)where the first term accounts for the probability of observing{circumflex over (β)}_(reg) due to the fit to the repeat transactionsobservations, and the second term accounts for the probability ofobserving {circumflex over (β)}_(reg) for the second difference of HPI.The last two terms account for the probability of observing the draws ofthe two refi premia given the process for the first difference of therefi premia, and D denotes the matrix which computes first differencesand the S_(refi) matrices selecting refi1 premia and refi2 premia fromβ.

This expression minimizes the sum of squared errors with errors weightedby the inverse of their respective variances. As more repeattransactions observations are added, the sum of squared pricing errorsadds more terms, while the sum of squared errors relating to innovationsin HPI and the refi premia may always have the same number of terms.Therefore, as more data becomes available, this data becomes moreimportant for fitting the model compared to the importance of minimizinginnovations in the HPI and refi premia generating process.

Minimizing expression (7) by writing down the Lagrangian, taking thefirst order conditions, and rearranging yields:{circumflex over (β)}_(reg)=(X′X+(σ_(ε) ²/σ_(ΔHPA) ²)D ² ′S _(HPI) ′S_(HPI) D ²+(σ_(ε) ²/σ_(refi) ²)D′S _(refi1) ′S _(refi1) D+(σ_(ε)²/σ_(refi) ²)D′S _(refi2) ′S _(ref2) D)⁻¹ S′yor {circumflex over(β)}_(reg) =Py.  (8)

Implementing this estimator may require using estimates or prior beliefsfor {circumflex over (σ)}_(ε) ²,{circumflex over (σ)}_(ΔHPI) ² and{circumflex over (σ)}_(refi) ² since these variances are not known.However, σ_(ε) ²/σ_(ΔHPA) ² and σ_(ε) ²/σ_(refi) ² may be thought of asthe above parameters. The regularized estimator {circumflex over(β)}_(reg)=Py is a linear estimator like the OLS estimator. Unlike theOLS estimator, however, the regularized estimator {circumflex over(β)}_(reg) optimally trades off fitting HPI to minimize repeattransaction return errors, innovations in the second difference of HPI,and innovations in the level of the two refi premia, given the relativevariances of these errors/innovations, With known error variances, theregularized estimator {circumflex over (β)}_(reg) is a maximumlikelihood (MLE) estimator that minimizes the mean squared error (MSE)of the estimated HPI to the underlying HPI.

After determining {circumflex over (β)}_(reg), which may be viewed as aregularized estimator, {circumflex over (β)}_(reg) may be used toestimate the values of HPI at time t₁ and t₂ and the values of refipremia at time t₁ and t₂. Using equation (8) or (9) above to determineregularized estimator {circumflex over (β)}_(reg) may reduce excess HPIgrowth volatility observed with OLS regressions and may improve the fitof the estimated HPI to the underlying HPI.

Accordingly, HPI(t) (hence HPI_(t2(i))) and HPI_(t1(i))) and REFI(t)(hence refi2 _(i)refiprem2 _(t2(i)) and refi1 _(i)refiprem1 _(t1(i)))may be calculated using regularized estimator {circumflex over(β)}_(reg). The resulting HPI(t) and REFI(t) may be outputted on display112 or to storage device 110 of FIG. 1. Using HPI(t) and REFI(t),property value growth I(t) may be calculated at the state, or anyaggregated level, using regularized estimator {circumflex over(β)}_(reg) in step 230.

In step 240 an estimation of the deviation between the aggregated levelindex, in this example the state level index, and the firstdisaggregated level index, is determined. For purposes of this example,the first disaggregated level index is the county level. The deviationsmay be determined using regularized estimators as discussed above. Themarked transactions from step 220, along with the aggregated level (e.g.state level) index are the inputs to step 240, When the deviations areestimated in step 240, they are then passed to step 250.

In step 240 a disaggregated (for example, county or zip code) model maybe fit to the repeat transaction return residual front the state levelmodel. Unlike the state level model where the HPI is assumed to follow arandom walk in first differences and refi premia are assumed to follow arandom walk in level the zip code level model assumes that zip codelevel HPI deviations from state HPI follow a random walk in levels andzip code level deviations in refi premia are given by period by periodindependent identically distributed (lid) shocks:y _(i)=log(p _(i,t2) /p _(i,t1))=HPI ^(s) _(t2(i)) −HPI ^(s)_(t1(i))+refi2_(i)refiprem2^(s) _(t2(i))−refi1_(i)refiprem1^(s) _(t1(i))+HPI ^(z) _(t2(i)) +HPI ^(z) _(t1(i))+refi2_(i)refiprem2^(z)_(t2(i))−refi1_(i)refiprem1^(z) _(t1(i))+ε_(i).HPI ^(z) _(t+1) =HPI ^(z) _(t)+η_(t+i) ^(HPIz).refiprem1^(z) _(t)=η_(t) ^(refi1z)refiprem2^(z) _(t)=η_(t) ^(refi2z).

Here superscript “s” indicates a state level variable and superscript“z” indicates a zip code level variable. State level variables evolve asdiscussed previously. The second stage zip code level regularized HPIestimator is analogous to the regularized HPI estimator at the statelevel, except that the regularization penalty functional form isrewritten to take into account the change in the order of differencingin HPI and refi premia.

In step 250, an adjusted WRSI for the first disaggregated level iscalculated by adjusting the aggregated level index, using theadjustments calculated in step 240. In this example, an adjusted WRSIfor the county level is created by calculating the repeat sales houseprice index function I(t) for the state by the estimated deviationsdetermined in step 240. The adjusted WRSI model may be expressed as:

$\begin{matrix}{{\ln\left( \frac{P_{i{({t + 1})}}}{{\hat{P}}_{i{({t + 1})}}} \right)} = {{\sum\limits_{j = 1}^{k}{\beta_{j}\left\lbrack {{\max\left( {0,{{date}_{i{({t + 1})}} - s_{j}}} \right)} - {\max\left( {0,{{date}_{it} - s_{j}}} \right)}} \right\rbrack}} + {\beta_{({k + 1})}R_{it}} + {\beta_{({k + 2})}R_{i{({t + 1})}}} + {\sum\limits_{j = 1}^{k}{\delta_{j}{\max\left( {0,{{date}_{it} - s_{j}}} \right\rbrack}R_{it}}} + {\sum\limits_{j = 1}^{k}{\varphi_{j}{\max\left( {0,{{date}_{i{({t + 1})}} - s_{j}}} \right)}R_{i{({t + 1})}}}} + e_{{it}{({t + 1})}}}} & (10)\end{matrix}$

The variable P_(i(t+1)) is the transaction value (i.e., the purchaseprice or appraised value) of house i (i=1, . . . , n) at time t+1 (t=1,. . . , T), {circumflex over (P)}_(i(t+1)) is the estimated transactionvalue (i.e., estimated purchase price or estimated appraisal value) ofhouse i (1=1, . . . , n) at time t+1 (t=1, . . . , T), estimated as thevalue of house i at time t inflated/deflated to time t+1 according tothe state level index, date_(it) is the purchase or refinance date ofhouse i (1=1, . . . , n) at time t (t=1, . . . , T), R_(it) is therefinance flag (0=purchase, 1=refinance) for transaction of house i(i=1, . . . , n) at time t (t=1, . . . , T), S_(j) is the knot point(specified as a date) for the j^(th) variable (j=1, . . . , k, where kis the number of quarters between 1975Q1 and current quarter), and βj,β_((k+1)), β_((k+2)) δj, φj are the model parameters (j=1, . . . , k,where k is the number of quarters between a starting quarter, such as1975Q1 and a current quarter).

The above-adjusted WRSI model not only calculates an adjusted index ofthe first disaggregated level using data from that level, but also usingdata from the aggregated level that contains the first disaggregatedlevel.

In step 260, an estimation of the deviation between the firstdisaggregated level index, in this example the county level index, and asecond disaggregated level index, is determined. For purposes of thisexample, the second disaggregated level index is the zip code level. Thedeviations may also be determined using regularized estimators asdiscussed above. The marked transactions from step 220, along with thefirst disaggregated (e.g. county level) index are the inputs to step260. When the deviations are estimated in step 260, they are then passedto step 270.

In step 270, an adjusted WRSI for the second disaggregated level iscreated by adjusting the first disaggregated level index, using theadjustments calculated in step 260. In this example, an adjusted WRSIfor the zip code level is created by calculating the repeat sales houseprice index function I(t) for the county by the estimated deviationsdetermined in step 260.

After the adjusted WRSI for the second disaggregated level (e.g. zipcode level) is calculated, the adjusted WRSI for the first disaggregatedlevel (e.g. county level) may be recalculated as a weighted average ofthe adjusted WRSI for the second disaggregated level in step 280.

Similarly, after the adjusted WRSI for the first disaggregated level(e.g. county level) is calculated, the adjusted WRSI for the aggregatedlevel (e.g., state level) may be recalculated as a weighted average ofthe adjusted WRSI for the first disaggregated level in step 290. Inaddition, any number of disaggregated levels may be calculated, and thenre-aggregated index values may also be calculated. For example, if acounty contains two zip codes with index values in a particular monththat are 100 for zip code 1 and 80 for zip code 2, and the weight is 75%for zip code 1 and 25% for zip code 2, the aggregate index value may becalculated by multiplying the index value and weight for zip code 1(e.g. 100*0.75=75), multiplying the index value and weight for zip code2 (e.g. 80*0.25=20), and added the two values (e.g. 75+20=95). Theweights may be based on the number of housing units in the geographicarea, the number of loans, dollar value of loans in the area, or otherweights. The weights may also be arithmetic or multiplicative (e.g.applied in logs).

Upon completion of the adjusted WRSI for each level (e.g. state, county,and zip code levels), the adjusted WRSI for each level may be outputtedon display 112 or to storage device 110 of FIG. 1 in step 295.

FIG. 3 illustrates exemplary plots of a conventional index estimator, aspline index estimator, and the regularized estimator with adjusted WRSIfor house price growth at particular levels (e.g. aggregated ordisaggregated) during a particular period of time (e.g., quarters). InFIG. 3, twenty one (21) quarters of home price levels, or index values,are plotted. As illustrated, the regularized estimator with adjustedWRSI produces an improved indication of changes in home price valueswhen compared with the conventional index estimator and the spline indexestimator.

The foregoing description of possible implementations and embodimentsconsistent with the present invention does not represent a comprehensivecatalog of all such implementations or all variations of theimplementations described. The description of only some implementationsshould not be construed as an intent to exclude other implementations,Other embodiments of the invention will be apparent to those skilled inthe art from consideration of the specification and practice of theinvention disclosed herein. One of ordinary skill in the art willunderstand how to implement the invention in the appended claims inother ways using equivalents and alternatives that do not depart fromthe scope of the following claims. It is intended that the specificationand examples be considered as exemplary only, with a true scope andspirit of the invention being indicated by the following claims.

What is claimed is:
 1. A computer-implemented method, performed by aprocessor connected to a communication network, a networked display, andnetworked real estate databases, the method comprising: collecting,using the processor accessing the networked real estate databases, dataregarding real estate transactions during a period of time, the realestate transactions comprising refinance and purchase transactions ofone or more real estate properties within a geographical region, andeach real estate transaction comprising an address of a real estateproperty associated with each real estate transaction, wherein theaddresses had been entered in a non-standardized format dependent on howthe addresses were listed for the corresponding real estatetransactions; converting, using the processor, addresses of the realestate properties into a standardized format; pairing, using theprocessor, a first transaction of a first real estate property completedat a first time point with a second transaction of a second real estateproperty completed at a second time point based on the standardizedaddresses, the first real estate property and the second real estateproperty having a same standardized address, and the first transactionand the second transaction comprising any combination of a refinancetransaction and a purchase transaction; determining, using theprocessor, value of the first real estate property by: determining,using the processor, repeat transaction return error, the repeattransaction return error being based on at least one of a value of arepeat sales house price index associated with an aggregated level atthe first time point or the second time point, a first transaction priceof the first transaction derived from the networked real estatedatabases, a second transaction price of the second transaction derivedfrom the networked-real estate databases, and a repeat transactionreturn noise derived from the networked real estate databases, whereinthe values of the repeat sales house price index, the first transactionprice, the second transaction price, and the repeat transaction returnnoise are derived from at least one of: data associated with the firsttransaction and the second transaction, regularized estimation data, orregularized with data associated with the first transaction and thesecond transaction; determining, using the processor, an estimate ofdeviation between the repeat sales house price index associated with theaggregated level and a repeat sales house price index associated with afirst disaggregated level, wherein the estimate of deviation is based onone or more repeat transaction returns derived from the networked realestate databases, a probability of the repeat transaction return noiseresulting in a change in the repeat sales house price index associatedwith the aggregated level, and a probability of the repeat transactionreturn noise resulting in a change in the repeat sales house price indexassociated with the first disaggregated level; determining, using theprocessor, a measure of refinance bias between the first time point andthe second time point, wherein the measure of refinance bias is derivedfrom a coefficient representing the first transaction refinance bias atthe first time point and a coefficient representing the secondtransaction refinance bias at the second time point; determining, usingthe processor, a measure of property value growth at the firstdisaggregated level at the first time point or the second time point,wherein the measure of property growth is determined based on optimizinga tradeoff between minimizing the repeat transaction return error,minimizing the estimate of deviation between the repeat sales houseprice index associated with the aggregated level and a repeat saleshouse price index associated with a first disaggregated level, andminimizing the measure of refinance bias between the first time-pointand the second time point; redetermining, using the processor, therepeat sales house price index associated with the aggregated level byweighing the measure of property value growth at the first disaggregatedlevel; and determining, using the processor, the value of the first realestate property based on the redetermined repeat sales house price indexassociated with the aggregated level; and generating, by the processor,a graph plotting changes in the measure of property value growth at thefirst disaggregated level at the first time point or the second timepoint and one or more graphs plotting corresponding changes in a measureof property value growth generated based on a conventional indexestimator and a spline index estimator, wherein the graph plottingchanges in the measure of property value growth at the firstdisaggregated level is updated based on: changes in the measure ofproperty value growth at the first disaggregated level as a deviationfrom changes in the measure of property value growth at the aggregatedlevel, and adjustments estimated from the aggregated level to the firstdisaggregated level by pairing a first real estate transaction to asecond real estate transaction using the repeat sales house price indexassociated with the aggregated level.
 2. The computer-implemented methodof claim 1, wherein determining the value of the first real estateproperty further comprises determining a regularized estimator in alinear fashion based on the one or more repeat transaction returns. 3.The computer-implemented method of claim 2, wherein the estimate ofdeviation is a regularized estimate of deviation.
 4. Thecomputer-implemented method of claim 1, wherein determining the value ofthe first real estate property further comprises calculating a repeatsales house price index associated with the first disaggregated levelbased on the estimate of deviation.
 5. The computer-implemented methodof claim 4, wherein determining the value of the first real estateproperty further comprises calculating a repeat sales house price indexassociated with a second disaggregated level based on the estimate ofthe deviation.
 6. The computer-implemented method of claim 5 wherein therepeat sales house price index function at the aggregated level, therepeat sales house price index function at the first disaggregatedlevel, and the repeat sales house price index function at the seconddisaggregated level are weighted to differentiate between purchasetransactions and refinance transactions.
 7. The computer-implementedmethod of claim 1, wherein determining the value of the first realestate property further comprises calculating a repeat sales house priceindex at the first disaggregated level based on a weighted average of adetermined regularized estimate of the deviation from a seconddisaggregated level.
 8. The computer-implemented method of claim 7,wherein the second disaggregated level is associated with a geographicregion within the United States of America or a zip code area.
 9. Thecomputer-implemented method of claim 7, wherein determining the value ofthe first real estate property further comprises calculating a repeatsales house price index at the aggregated level based on a weightedaverage of a determined regularized estimate of the deviation from thefirst disaggregated level.
 10. The computer-implemented method of claim1, wherein the aggregated level is a geographic region within the UnitedStates of America or a state.
 11. The computer-implemented method ofclaim 1, wherein the first disaggregated level is a geographic regionwithin the United States of America or a county.
 12. A systemcomprising: a processor connected to a communication network, anetworked display, and a networked real estate databases; and a memorydevice containing instructions which, when executed, causes the systemto perform a method comprising: collecting, using the processoraccessing the networked real estate databases, data regarding realestate transactions during a period of time, the real estatetransactions comprising refinance and purchase transactions of one ormore real estate properties within a geographical region, and each realestate transaction comprising an address of a real estate propertyassociated with each real estate transaction, wherein the addresses hadbeen entered in a non-standardized format dependent on how the addresseswere listed for the corresponding real estate transactions; converting,using the processor, addresses of the real estate properties into astandardized format; pairing, using the processor, a first transactionof a first real estate property completed at a first time point with asecond transaction of a second real estate property completed at asecond time point based on the standardized addresses, the first realestate property and the second real estate property having a samestandardized address, and the first transaction and the secondtransaction comprising any combination of a refinance transaction and apurchase transaction; determining, using the processor, value of thefirst real estate property by: determining, using the processor, repeattransaction return error, the repeat transaction return error beingbased on at least one of a value of a repeat sales house price indexassociated with an aggregated level at the first time point or thesecond time point, a first transaction price of the first transactionderived from the networked database, a second transaction price of thesecond transaction derived from the networked real estate databases, anda repeat transaction return noise derived from the networked real estatedatabases, wherein the value of the repeat sales house price index, thefirst transaction price, the second transaction price, and the repeattransaction return noise are derived from at least one of: dataassociated with the first transaction and the second transaction,regularized estimation data, or regularized with data associated withthe first transaction and the second transaction; determining, using theprocessor, an estimate of deviation between the repeat sales house priceindex associated with the aggregated level and a repeat sales houseprice index associated with a first disaggregated level, wherein theestimate of deviation is based on one or more repeat transaction returnsderived from the networked real estate databases, a probability of therepeat transaction return noise resulting in a change in the repeatsales house price index associated with the aggregated level, and aprobability of the repeat transaction return noise resulting in a changein the repeat sales house price index associated with the firstdisaggregated level; determining, using the processor, a measure ofrefinance bias between the first time point and the second time-point,wherein the measure of refinance bias is derived from a coefficientrepresenting the first transaction refinance bias at the first timepoint and a coefficient representing the second transaction refinancebias at the second time point; determining, using the processor, ameasure of property value growth at the first disaggregated level at thefirst time point or the second time point, wherein the measure ofproperty growth is determined based on optimizing a tradeoff betweenminimizing the repeat transaction return error, minimizing the estimateof deviation between the repeat sales house price index associated withthe aggregated level and a repeat sales house price index associatedwith a first disaggregated level, and minimizing the measure ofrefinance bias between the first time-point and the second time point;redetermining, using the processor, the repeat sales house price indexassociated with the aggregated level by weighing the measure of propertyvalue growth at the first disaggregated level; and determining, usingthe processor, the value of the first real estate property based on theredetermined repeat sales house price index associated with theaggregated level; and generating, by the processor, a graph plottingchanges in the measure of property value growth at the firstdisaggregated level at the first time point or the second time point andcorresponding changes in a measure of property value growth generatedbased on a conventional index estimator and a spline index estimator,wherein the graph plotting changes in the measure of property valuegrowth at the first disaggregated level is updated based on: changes inthe measure of property value growth at the first disaggregated level asa deviation from changes in the measure of property value growth at theaggregated level, and adjustments estimated from the aggregated level tothe first disaggregated level by pairing a first real estate transactionto a second real estate transaction using the repeat sales house priceindex associated with the aggregated level.
 13. The system of claim 12,wherein determining the value of the first real estate property furthercomprises determining a regularized estimator in a linear fashion basedon the one or more repeat transaction returns.
 14. The system of claim13, wherein the estimate of deviation is a regularized estimate ofdeviation.
 15. The system of claim 12, wherein determining the value ofthe first real estate property further comprises calculating a repeatsales house price index associated with the first disaggregated levelbased on the estimate of deviation.
 16. The system of claim 15, whereindetermining the value of the first real estate property furthercomprises calculating a repeat sales house price index associated with asecond disaggregated level based on the estimate of the deviation. 17.The system of claim 16, wherein the repeat sales house price indexfunction at the aggregated level, the repeat sales house price indexfunction at the first disaggregated level, and the repeat sales houseprice index function at the second disaggregated level are weighted todifferentiate between purchase transactions and refinance transactions.18. The system of claim 12, wherein determining the value of the firstreal estate property further comprises calculating a repeat sales houseprice index at the first disaggregated level based on a weighted averageof a determined regularized estimate of the deviation from a seconddisaggregated level.
 19. The system of claim 18, wherein the seconddisaggregated level is associated with a geographic region within theUnited States of America or a zip code area.
 20. The system of claim 18,wherein determining the value of the first real estate property furthercomprises calculating a repeat sales house price index at the aggregatedlevel based on a weighted average of a determined regularized estimateof the deviation from the first disaggregated level.
 21. The system ofclaim 12, wherein the aggregated level is a geographic region within theUnited States of America or a state.
 22. The system of claim 12, whereinthe first disaggregated level is a geographic region within the UnitedStates of America or a county.
 23. A non-transitory computer-readablestorage medium including program instructions for performing, whenexecuted by a processor connected to a communication network, anetworked display, and a networked real estate databases, a methodcomprising: collecting, using the processor accessing the networked realestate databases, data regarding real estate transactions during aperiod of time, the real estate transactions comprising refinance andpurchase transactions of one or more real estate properties within ageographical region, and each real estate transaction comprising anaddress of a real estate property associated with each real estatetransaction, wherein the addresses had been entered in anon-standardized format dependent on how the addresses were listed forthe corresponding real estate transactions; converting, using theprocessor, addresses of the real estate properties into a standardizedformat; pairing, using the processor, a first transaction of a firstreal estate property completed at a first time point with a secondtransaction of a second real estate property completed at a second timepoint based on the standardized addresses, the first real estateproperty and the second real estate property having a same standardizedaddress, and the first transaction and the second transaction comprisingany combination of a refinance transaction and a purchase transaction;determining, using the processor, value of the first real estateproperty by: determining, using the processor, repeat transaction returnerror, the repeat transaction return error being based on at least oneof a value of a repeat sales house price index associated with anaggregated level at the first time point or the second time point, afirst transaction price of the first transaction derived from thenetworked real estate databases, a second transaction price of thesecond transaction derived from the networked-real estate databases, anda repeat transaction return noise derived from the networked real estatedatabases, wherein the value of the repeat sales house price index, thefirst transaction price, the second transaction price, and the repeattransaction return noise are derived from at least one of: dataassociated with the first transaction and the second transaction,regularized estimation data, or regularized with data associated withthe first transaction and the second transaction; determining, using theprocessor, an estimate of deviation between the repeat sales house priceindex associated with the aggregated level and a repeat sales houseprice index associated with a first disaggregated level, wherein theestimate of deviation is based on one or more repeat transaction returnsderived from the networked real estate databases, a probability of therepeat transaction return noise resulting in a change in the repeatsales house price index associated with the aggregated level, and aprobability of the repeat transaction return noise resulting in a changein the repeat sales house price index associated with the firstdisaggregated level; determining, using the processor, a measure ofrefinance bias between the first time point and the second time point,wherein the measure of refinance bias is derived from a coefficientrepresenting the first transaction refinance bias at the first timepoint and a coefficient representing the second transaction refinancebias at the second time point; determining, using the processor, ameasure of property value growth at the first disaggregated level at thefirst time point or the second time point, wherein the measure ofproperty growth is determined based on optimizing a tradeoff betweenminimizing the repeat transaction return error, minimizing the estimateof deviation between the repeat sales house price index associated withthe aggregated level and a repeat sales house price index associatedwith a first disaggregated level, and minimizing the measure ofrefinance bias between the first time-point and the second time point;redetermining, using the processor, the repeat sales house price indexassociated with the aggregated level by weighing the measure of propertyvalue growth at the first disaggregated level; and determining, usingthe processor, the value of the first real estate property based on theredetermined repeat sales house price index associated with theaggregated level; and generating, by the processor, a graph plottingchanges in the measure of property value growth at the firstdisaggregated level at the first time point or the second time point andcorresponding changes in a measure of property value growth generatedbased on a conventional index estimator and a spline index estimator,wherein the graph plotting changes in the measure of property valuegrowth at the first disaggregated level is updated based on: changes inthe measure of property value growth at the first disaggregated level asa deviation from changes in the measure of property value growth at theaggregated level, and adjustments estimated from the aggregated level tothe first disaggregated level by pairing a first real estate transactionto a second real estate transaction using the repeat sales house priceindex associated with the aggregated level.
 24. The non-transitorycomputer-readable storage medium of claim 23, wherein determining thevalue of the first real estate property further-comprises determining aregularized estimator in a linear fashion based on the one or morerepeat transaction returns.
 25. The non-transitory computer-readablestorage medium of claim 24, wherein the estimate of deviation is aregularized estimate of deviation.
 26. The non-transitorycomputer-readable storage medium of claim 23, wherein determining thevalue of the first real estate property further-comprises calculating arepeat sales house price index associated with the first disaggregatedlevel based on the estimate of deviation.
 27. The non-transitorycomputer-readable storage medium of claim 26, wherein determining thevalue of the first real estate property further-comprises calculating arepeat sales house price index associated with a second disaggregatedlevel based on the estimate of the deviation.
 28. The non-transitorycomputer-readable storage medium of claim 27, wherein the repeat saleshouse price index function at the aggregated level, the repeat saleshouse price index function at the first disaggregated level, and therepeat sales house price index function at the second disaggregatedlevel are weighted to differentiate between purchase transactions andrefinance transactions.
 29. The non-transitory computer-readable storagemedium of claim 23, wherein determining the value of the first realestate property further-comprises calculating a repeat sales house priceindex at the first disaggregated level based on a weighted average of adetermined regularized estimate of the deviation from a seconddisaggregated level.
 30. The non-transitory computer-readable storagemedium of claim 29, wherein the second disaggregated level is associatedwith a geographic region within the United States of America or a zipcode area.
 31. The non-transitory computer-readable storage medium ofclaim 29, wherein determining the value of the first real estateproperty further-comprises calculating a repeat sales house price indexat the aggregated level based on a weighted average of a determinedregularized estimate of the deviation from the first disaggregatedlevel.
 32. The non-transitory computer-readable storage medium of claim23, wherein the aggregated level is a geographic region within theUnited States of America or a state.
 33. The non-transitorycomputer-readable storage medium of claim 23, wherein the firstdisaggregated level is a geographic region within the United States ofAmerica or a county.